Aerodynamic forces are commonly used by automotive engineers to enhance automobile performance, safety, and fuel economy. Engineers shape the body contour of an automobile to create and enhance certain aerodynamic forces. In one example, many racing and high-performance automobiles are equipped with rear spoilers that produce downforce or “negative lift” proximate the rear end of the vehicle. Such downforce improves the automobile's traction or ability to hold the road. However, in addition to adding desirable downforce, rear spoilers sometimes add performance-reducing drag to the automobile. This trade-off effectively illustrates the need for automotive engineers to have a detailed picture of the aerodynamic forces acting on a vehicle in motion.
FIG. 1 depicts an exemplary automobile 100 (e.g., a racecar) for illustrating a coordinate axis that is commonly used to model aerodynamic forces acting on an automobile in motion. The depicted coordinate axis is centered at the automobile's center of gravity (“CG”). An x-axis proceeds from the CG along the longitudinal axis of the automobile as shown. A y-axis proceeds in a lateral direction perpendicular to the longitudinal axis of the automobile. A z-axis proceeds in a vertical direction perpendicular to both the x- and y-axes as shown. The depicted coordinate system is used herein to describe embodiments of the present invention.
The primary aerodynamic forces acting on a moving automobile (or on an automobile placed in a wind tunnel) are drag, positive and negative sideforce, lift, and downforce (negative lift). In view of the depicted coordinate axes, drag is applied to the automobile in a direction along the negative x-axis. Positive and negative sideforces are applied in directions along the positive and negative y-axis respectively. Lift is applied in a direction along the negative z-axis while downforce is applied in a direction along the positive z-axis. The primary aerodynamic moments acting on a moving automobile are roll, pitch, and yaw. Roll is the moment defined about the x-axis, pitch is the moment defined about the y-axis, and yaw is the moment defined about the z-axis.
Air moving over an automobile produces pressure gradients and viscous friction that combine to create aerodynamic forces and moments applied in each of the directions noted above. The precise nature of the aerodynamic forces applied to the automobile depends on a variety of factors including the velocity and density of the air flow, the shape of the automobile, and the orientation of the automobile relative to the direction of the air flow.
When an automobile corners it must rotate about its z-axis and translate its center of mass along an arc. In this regard, the automobile's direction of motion becomes angled or “yawed” relative to an incoming airflow. An automobile may also become yawed relative to the incoming airflow when the automobile encounters a crosswind or when the automobile is yawed in a wind tunnel. This yawed orientation is illustrated in FIG. 2A. Streamlines 105 provide a visual illustration of the airflow as it travels around the automobile body 200. The airflow approaches the automobile 200 in a direction defined by flow arrow F as shown. The automobile 200 includes an imaginary longitudinal axis 150 that divides the automobile 200 and the area around the automobile into two parts, namely, a passenger side 115 and a driver side 110. The automobile 200 also includes a leading edge and a trailing edge defined by lines A and B, respectively. The longitudinal axis 150 of the depicted automobile 200 is yawed relative to the incoming air flow by an angle θ.
FIG. 2B provides a simplified illustration of the relative pressures applied to the yawed automobile 200 depicted in FIG. 2A. Relative pressure profiles for air passing over the driver and passenger sides of the automobile are shown by plotting the pressure coefficient Cp (non-dimensionalized pressure) for locations along each side of the automobile versus a distance x from the leading edge of the automobile along the x-axis for each locations. The distances x along the x-axis are also non-dimensionalized by dividing the distance by the length of the automobile L. The pressure coefficient axis in the graph has been inverted as is conventional. The pressure profile around each side of the automobile when the yaw angle θ equals zero is represented by a solid line and the pressure profiles when the automobile is yawed at a negative (counter-clockwise) yaw angle relative to the incoming airflow F are represented by dashed lines.
Turning first to the passenger side pressure coefficient profile PP when the automobile is yawed (as represented by the dashed-dotted line), as the air moves from the front end of the automobile around its right front quarter-panel the pressure is reduced (i.e., becomes more negative) and then plateaus along the side of the automobile. As air moves from the right rear quarter panel around the rear end of the automobile the airflow separates from the vehicle and the pressure drops again. Turning to the driver side pressure profile DP, the pressure decreases rapidly as the air flow is separated from the automobile when rounding the corner defined between the front end of the automobile and the left front quarter-panel as shown.
The aerodynamic pressures of a yawed automobile 200, such as the pressures illustrated in FIG. 2B, often have a net effect of producing a moment applied to the automobile 200 about the center of gravity. As illustrated in FIG. 2B, when the automobile 200 is oriented at a negative yaw angle relative to an incoming airflow the pressure produced proximate the front driver side of the automobile is generally much lower than the pressure produced proximate the front of the passenger side. As a result, a negative yawing moment YM is applied to the automobile 200 as illustrated in FIG. 3A. Positioning a symmetric automobile at a positive yaw angle relative to an incoming airflow has the opposite effect, creating a positive yawing moment about the automobile's CG. Any yawing moments caused by the aerodynamic forces must generally be resisted by friction occurring between the automobile's wheels and the road surface to maintain the automobile on its intended path.
Additional forces, apart from aerodynamic forces, also act on a cornering automobile. For example, when an automobile is cornering, the automobile's forward inertia tends to carry it forward in a straight line. To overcome the automobile's inertia and maintain the automobile on a cornering trajectory, a centripetal force is generally provided by friction occurring between the automobile's wheels and the road surface.
FIG. 3B illustrates a front view of the automobile 200 making a left-hand turn. The forces 300 applied to the automobile from the tires gripping the road are directed towards the inside of the turn. These forces are located below the automobile's center of gravity and therefore cause a positive rolling moment 302. This rolling moment 302 is usually undesirable in that it makes the vehicle more prone to a rollover and also reduces the weight or downward pressure on the inside tires 303 thereby reducing the ability of the inside tires 303 to grip the road.
FIG. 3C also illustrates the automobile 200 traveling around a left-hand corner. As described above, the four tires must provide the centripetal force toward the inside of the turn in order to allow the car to travel along the arc of the turn. Depending on many factors, such as how the vehicle enters the turn and how the throttle is applied, the rear tires 304 may be required to produce a greater side force 306 than side force 307 required of the front tires 305, or vice versa. As also described above with respect to FIG. 3A, the aerodynamic forces on the cornering automobile making a left-hand turn often result in a negative yawing moment 308 that increases the force 306 that rear tires 304 must resist and decrease the force 307 that the front tires 305 must resist. In high speed racing applications, the combination of the negative yawing moment 308 and the automobile's inertia may exceed the tires' ability to grip the surface of the road resulting in a slide or a “spin-out” of the racecar.
For example, if the magnitude of the side force 306 required of the rear tires 304 is greater than the side force that the rear tires 304 can withstand, the rear of the vehicle will slide toward the outside of the turn, potentially resulting in a spin-out of the automobile. This is generally referred to as “oversteer.” A driver may describe a car that is more prone to oversteer as being “loose.” Alternatively, if the magnitude of the side force 307 required of the front tires 305 is greater than the side force that the front tires 305 can withstand, the front of the vehicle will slide toward the outside of the turn or the vehicle will simply continue in a straight line and not follow the arc of the turn. This is generally referred to as “understeer.” A driver may describe a car that is more prone to understeer as being “tight.” However, even if the tires can effectively resist the yawing moments and the inertial energy produced during cornering without causing the automobile to over or under steer, the high heat and friction that results in the tires may prematurely degrade and wear some or all of the tires.
Horizontal wing devices or protruding air deflection devices often referred to as “spoilers” have been used on automobiles for purposes of creating additional downforce or reducing the vehicle's tendency to lift during certain operating conditions. Such horizontal wing devices generally have an inverted airfoil cross-section and have frequently been mounted on a rearward portion of an automobile, in order to provide improved rear-wheel traction and other enhanced handling characteristics at high speeds. These horizontal wings are generally not configured to provide a significant sideforce and are not intended for altering the yawing or rolling moments of the automobile.
It would be desirable then to provide an automobile design that tends to produce a more favorable yawing moment, rolling moment, and/or sideforce in order to reduce the stress on the tires during high speed cornering and/or in order to improve the handling characteristics of the automobile. It is also generally preferred that the body of the automobile appear generally symmetrical and aesthetically pleasing.